if the theory is that sexual orientation discrimination is a form of sex discrimnation?

Many proponents of same-sex marriage rely (at least in part) on this theory, and at least one judge has accepted it. If Jane is barred from marrying Kate but is allowed to marry Larry, the argument goes, that's sex discrimination -- the law is considering Jane's, Kate's, and Larry's sex in deciding whom they may marry. Under similar circumstances, bans on interracial marriage are treated as race discrimination; therefore, bans on same-sex marriage should be treated as sex discrimination. Let's assume that this argument is indeed accepted, and courts hold that traditional marriage rules violate the Equal Protection Clause (or a state Equal Rights Amendment).

It seems to me that exactly the same argument would be available as to discrimination by private parties, under statutes that bar sex discrimination. If sexual orientation discrimination is logically sex discrimination under constitutional rules, then it would be sex discrimination under statutory rules.

After all, antidiscrimination law bars employers from firing people for dating outside their race. Under the logic of the Jane/Kate/Larry argument, the sex discrimination branch of that law would likewise bar employers from firing people for dating within their own sex. And the same would apply to housing, public accommodations, and any other places where sex discrimination is banned (though probably not scouting organizations, at least so long as the Girl Scouts can remain the Girl Scouts).

Nonetheless, I would think that quite a few people who are open to government recognition of same-sex marriage would be quite hesitant to create more restriction on private employers: For instance, the former would make lots of sense to many libertarians, but the latter would not. Moreover, some people who only mildly oppose same-sex marriage (for instance, because they recognize that the matter is largely symbolic, and that it makes little real difference to them whether same-sex couples are allowed to marry) might much more strongly oppose a new set of antidiscrimination laws, which would indeed restrict others' freedom of action. Yet while judges might conclude that sexual orientation discrimnation is sex discrimnation for Equal Protection Clause purposes but not for statutory purposes, others (perhaps enough to affect the result) may disagree.

Have you folks seen this being used as an argument, either for accepting this theory to justify a right to same-sex marriage (look, we can get bans on private discrimination this way, too!), or for rejecting this theory (if you accept it as to same-sex discrimination, then private discrimination will be banned, too!)? If you have, please post a pointer in the comments.

Please do not use the comments to discuss other arguments for or against same-sex marriage, or for or against antidiscrimination law, or for that matter the sexual orientation discrimination = sex discrimination argument on its own merits. I'd like to focus the discussion on the potential causal relationship between this argument and restrictions on nongovernmental discrimination. Many thanks.